Using notify-send with cron

You need to set the DBUS_SESSION_BUS_ADDRESS variable. By default cron does not have access to the variable. To remedy this put the following script somewhere and call it when the user logs in, for example using awesome and the run_once function mentioned on the wiki. Any method will do, since it does not harm if the function is called more often than required.

#!/bin/sh

touch $HOME/.dbus/Xdbus
chmod 600 $HOME/.dbus/Xdbus
env | grep DBUS_SESSION_BUS_ADDRESS > $HOME/.dbus/Xdbus
echo 'export DBUS_SESSION_BUS_ADDRESS' >> $HOME/.dbus/Xdbus

exit 0

This creates a file containing the required Dbus evironment variable. Then in the script called by cron you import the variable by sourcing the script:

if [ -r "$HOME/.dbus/Xdbus" ]; then
  . "$HOME/.dbus/Xdbus"
fi

Here is an answer that uses the same mechanism.

You need to set the variables in the crontab itself:

DISPLAY=:0.0
XAUTHORITY=/home/matrix/.Xauthority

# m h  dom mon dow   command 
* * * * *  /usr/bin/notify-send "hello"

No sudo needed, at least not on my system.

The safest way to get X session related environmental variables is to get them from the environment of a process of the user who is logged on to X. Here is an adaptation of the script that I use for exactly the same purpose (although DBUS_SESSION_BUS_ADDRESS doesn't seem to be a problem for me on Debian):

X=Xorg                   # works for the given X command
copy_envs="DISPLAY XAUTHORITY DBUS_SESSION_BUS_ADDRESS"

tty=$(ps h -o tty -C $X | head -1)
[ -z "$tty" ] && exit 1

# calling who with LANG empty ensures a consistent date format
who_line=$(LANG= who -u | grep "^[^ ]\+[ ]\+$tty")

x_user=$(echo $who_line | cut -d ' ' -f 1)  # the user associated with the tty
pid=$(echo $who_line | cut -d ' ' -f 7)     # the user's logon process

for env_name in $copy_envs
do
  # if the variable is not set in the process environment, ensure it does not remain exported here
  unset "$env_name"

  # use the same line as is in the environ file to export the variable
  export "$(grep -az "^$env_name=" /proc/$pid/environ)" >/dev/null
done

sudo -u "$x_user" notify-send "hello"

This sends to message to the first X user it finds, although you could add a loop to send it to all users.

Update

It seems that updates to the utmp format cause who to print a display instead of a tty in its second column. This actually makes things easier, previously it only printed the display in the comment at the end and I decided this wasn't safe to rely on for the original answer. If this is the case, try this:

X=Xorg                   # works for the given X command
copy_envs="DISPLAY XAUTHORITY DBUS_SESSION_BUS_ADDRESS"

# calling who with LANG empty ensures a consistent date format
who_line=$(LANG= who -u | awk '$2 ~ ":[0-9]"')

x_user=$(echo $who_line | cut -d ' ' -f 1)  # the user associated with the tty
pid=$(echo $who_line | cut -d ' ' -f 7)     # the user's logon process

for env_name in $copy_envs
do
  # if the variable is not set in the process environment, ensure it does not remain exported here
  unset "$env_name"

  # use the same line as is in the environ file to export the variable
  export "$(grep -az "^$env_name=" /proc/$pid/environ)" >/dev/null
done

sudo -u "$x_user" notify-send "hello"